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GATE EC Networks, Signals and Systems questions

Practise Networks, Signals and Systems questions for GATE EC. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify whether the signal and system are continuous-time or discrete-time. Check linearity, time invariance and stability before selecting a transform or response method.

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Official PYQ2023Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
In the circuit shown below, the current ii flowing through 200  Ω200 \; \Omega resistor is___________ mA\mathrm{mA} (rounded off to two decimal places).
Official PYQ2023Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
For the two port network shown below, the [Y]–[\mathrm{Y}] –parameters is given as [Y]=1100[2−1−14/3]S[Y]=\frac{1}{100}\left[\begin{array}{cc}2 & -1 \\ -1 & 4 / 3\end{array}\right] S The value of load impedance ZL,\mathrm{Z}_{\mathrm{L},} in Ω\Omega, for maximum power transfer will be ____________ (rounded off to the nearest integer).
Official PYQ2023Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
In the circuit shown below, switch S\mathrm{S} was closed for a long time. If the switch is opened at t=0t=0, the maximum magnitude of the voltage VR,in volts,\mathrm{V}_{\mathrm{R}}, \text{in volts,} is_____________ (rounded off to the nearest integer).
Official PYQ2023Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
The switch S1\mathrm{S}_{1} was closed and S2\mathrm{S}_{2} was open for a long time. At t=0t=0, switch S1\mathrm{S}_{1} is opened and S2\mathrm{S}_{2} is closed, simultaneously. The value of ic(0+)\mathrm{i}_{\mathrm{c}}\left(0^{+}\right), in amperes, is
Official PYQ2023Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
The h\text{h}-parameters of a two port network are shown below. The condition for the maximum small signal voltage gain Vout Vs\frac{\mathrm{V}_{\text{out }}}{\mathrm{V}_{\mathrm{s}}} is
Official PYQ2023Networks, Signals and SystemsDiscrete-time SignalsMCQ · 2 marks
Consider a discrete-time periodic signal with period N=5N=5. Let the discrete-time Fourier series (DTFS\text{(DTFS}) representation be x[n]=∑k=04akejk2πn5x[n]=\sum_{k=0}^4 a_k e^{\frac{j k 2 \pi n}{5}}, where a0=1,a1=a_0=1, a_1= 3j,a2=2j,a3=−2j3 j, a_2=2 j, a_3=-2 j and a4=−3ja_4=-3 j. The value of the sum ∑n=04x[n]sin⁡4πn5\sum_{n=0}^4 x[n] \sin \frac{4 \pi n}{5} is
Official PYQ2023Networks, Signals and SystemsLTI SystemsMCQ · 2 marks
Let an input x[n]x[n] having discrete-time Fourier transform X(ejΩ)=1−e−jΩ+2e−3jΩX\left(e^{j \Omega}\right)=1-e^{-j \Omega}+2 e^{-3 j \Omega} be passed through an LTI system. The frequency response of the LTI system is H(ejΩ)=1−12e−j2ΩH\left(e^{j \Omega}\right)=1-\frac{1}{2} e^{-j 2 \Omega}. The output y[n]y[n] of the system is
Official PYQ2023Networks, Signals and SystemsLTI SystemsMCQ · 2 marks
Let x(t)=10cos⁡(10.5Wt)x(t)=10 \cos (10.5 W t) be passed through an LTI system having impulse response h(t)=π(sin⁡Wtπt)2cos⁡10Wth(t)=\pi\left(\frac{\sin W t}{\pi t}\right)^{2} \cos 10 Wt. The output of the system is
Official PYQ2023Networks, Signals and SystemsContinuous-time SignalsMCQ · 2 marks
Let x1(t)\mathrm{x}_1(\mathrm{t}) and x2(t)\mathrm{x}_2(\mathrm{t}) be two band-limited signals having bandwidth B=4π×103  rad/sB=4 \pi \times 10^3 \; \mathrm{rad} / \mathrm{s} each. In the figure below, the Nyquist sampling frequency, in rad/s\mathrm{rad} / \mathrm{s}, required to sample y(t)y(\mathrm{t}), is
Official PYQ2023Networks, Signals and SystemsLTI SystemsNAT · 2 marks
Let x1(t)=u(t+1.5)−u(t−1.5)\mathrm{x}_1(\mathrm{t})=\mathrm{u}(\mathrm{t}+1.5)-\mathrm{u}(\mathrm{t}-1.5) and x2(t)\mathrm{x}_2(\mathrm{t}) is shown in the figure below. For y(t)=x1(t)∗x2(t)\mathrm{y}(\mathrm{t})=\mathrm{x}_1(\mathrm{t}) * \mathrm{x}_2(\mathrm{t}), the ∫−∞∞y(t)dt\int_{-\infty}^{\infty} \mathrm{y}(\mathrm{t}) \mathrm{dt} is ______________ (rounded off to the nearest integer).
Official PYQ2023Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
In the circuit below, the voltage VLV_L is _________ V\mathrm{V} (rounded off to two decimal places).
Official PYQ2022Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
The current II in the circuit shown is ______________.
Official PYQ2022Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
Consider the circuit shown in the figure. The current II flowing through the 10  Ω10 \; \Omega resistor is _____________.
Official PYQ2022Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
The Fourier transform X(jω)X(j \omega) of the signal x(t)=t(1+t2)2x(t) = \frac{t}{(1+t^{2})^{2}} is ______________.
Official PYQ2022Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
The frequency response H(f)H(f) of a linear time-invariant system has magnitude as shown in the figure. Statement I:\text{I}: The system is necessarily a pure delay system for inputs which are bandlimited to −α≤f≤α.- \alpha \leq f \leq \alpha. Statement II:\text{II}: For any wide-sense stationary input process with power spectral density Sx(f),S_{x}(f), the …
Official PYQ2022Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes)\text{(in Amperes)} through the resistor is 2sin⁡(t+π/2).2\sin (t+\pi/2). The displacement current (in Amperes)\text{(in Amperes)} through the capacitor is ______________.
Official PYQ2022Networks, Signals and SystemsLTI SystemsNAT · 1 mark
Let x1(t)=e−tu(t)x_{1} (t) = e^{-t}u(t) and x2(t)=u(t)–u(t–2),x_{2}(t) = u(t) – u(t – 2), where u(⋅)u(\cdot) denotes the unit step function. If y(t)y(t) denotes the convolution of x1(t)x_{1}(t) and x2(t),x_{2}(t), then lim⁡t→∞y(t)=\displaystyle \lim_{t \rightarrow \infty} y(t) = ______________ (rounded off to one decimal place).
Official PYQ2022Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
For the circuit shown, the locus of the impedance Z(jω)Z (j \omega) is plotted as ω\omega increases from zero to infinity. The values of R1R_{1} and R2R_{2} are:
Official PYQ2022Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
Consider the circuit shown in the figure with input V(t)V(t) in volts. The sinusoidal steady state current I(t)I(t) flowing through the circuit is shown graphically (where tt is in seconds). The circuit element ZZ can be ____________.
Official PYQ2022Networks, Signals and SystemsLTI SystemsMSQ · 2 marks
The outputs of four systems (S1,S2,S3,(S_{1}, S_{2}, S_{3}, and S4)\text{S}_{4}) corresponding to the input signal sin⁡(t),\sin(t), for all time t,t, are shown in the figure. Based on the given information, which of the four systems is/are definitely NOT LTI\text{NOT LTI} (linear and time-invariant)?